What is the purpose of setting the first derivative equal to zero in the optimiz

Question

What is the purpose of setting the first derivative equal to zero in the optimization process? Suppose you are optimizing a function with the highest power of 3, describe how you would determine whether a max, min, or inflection point. Provide an example. Suppose the price and quantity equilibrium is below the price and quantity which maximizes total revenue, what strategy would you use for the firm. Assume that the demand curve is downward sloping. Suppose the firm is operating in the inelastic portion of its demand curve, what strategy would you use to increase the firm's total revenue. Interpret the results of the Jarque-Bera] Statistic for a series' descriptive statistic is 0.5140?

Explanation / Answer

1.

The main purpose of optimization is to get the minimum or maximum value of the function and we know that for any function having maximum or minimum level ,its first derivative should be zero as derivative of function measures slope.So that means as we are concerned with getting level of minimum costs or maximum profits, we should have first derivative zero.

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